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COPYRIGHT DEPOSIT. 













» 




























/ 

























Scoates* 

Agricultural Surveying 
Laboratory 
Manual 













I 



Scoates’ 

Agricultural Surveying 
Laboratory Manual 

L )>i> 

-' 77 / <7 


Daniels Scoates, a. e. 

' 1 

Professor Agricultural Engineering, Mississippi Agricultural 

and Mechanical College 

Member American Society Agricultural 
Engineers 


S econ d-Edition 


AGRICULTURAL COLLEGE, MISSISSIPPI 
1918 






COPYRIGHTED, 1913 AND 1918 
BY 

D. SCOATES 





i.. 


©Cl. A 5 13 98 7 

APR -5 1919 

—yu>, /, 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 


INDEX 


Introduction, .5 

Investigating Pace,.9 

Chaining Distances,.9 


Determining Angles With the Tape, ... 10 

Computing Area of Triangles,.11 

Laying Out Buildings (Tape),.12 


Differential Leveling, . 12 

Profile Leveling,.13 

Reading Angles With Instrument, ... 14 

Topographical Surveying,.15 

Designing Drainage Systems,.15 

Tile Intersection,.16 

Terracing,.16 

Laying Out Building (Instrument), ... 17 

Adjusting Level,.18 


Specimen Laboratory Notes,.25-41 

Determining Size of Angle With Tape, . . 73 

Laying Off a Right Angle With Tape, . . 75 

Laying Off Any Angle With Tape, .... 78 

Table of Areas Drained by Tile, .... 80 


Tile Drainage Estimating,.81 

Computing Areas,.86 

Tables of Measurement,.89 

Logarithms of Numbers,.91 

Natural Sines,.94 

Natural Tangents,.97 






















« 










































AGRICULTURAL SURVEYING LABORATORY 


5 


INTRODUCTION 


This Manual is primarily written for agricul¬ 
tural students attending agricultural colleges. The 
principal thing kept in mind in selecting, compiling 
and arranging the Exercises, was to stress only 
those things which are necessary to a thorough un¬ 
derstanding of surveying needs as are found on the 
average farm. 

The Manual is divided into four parts: (1). The 
part giving the assignments for the different work 
to be done. (2). Sample pages showing how the 
laboratory work should be written up. (3). Blank 
pages on which the student is to write up his work. 
(4). Tables of information useful to the student in 
this laboratory work. 

Each student should have a Manual, and as soon 
as he gets it he should write his name in ink on it, 
thus insuring its return in case of loss. 

Make a practice of writing up each day’s notes 
in a complete form the day they are taken. This 
will prevent the complete loss of a record of the 
day’s work if one of the party should lose his book. 

Don’t fudge your notes. This is only stealing 
from yourself. While it may get you past the in- 
structor^ yet it does not give you the practice you 
are taking this course to receive. It is better not to 
make any erasures in your note book, but rather to 
cross out the mistake, thus avoiding the appearance 
of fudging. All notes should be neatly lettered and 
not written. 

The note book should be handed in to the in¬ 
structor for inspection on the following dates:. 














* 







V 



. 

4 





















AGRICULTURAL SURVEYING LABORATORY 


7 


PARTIES 

The classes shall divide themselves up in parties 
of three each. Each party shall elect a captain who 
shall turn in the names of his party to the instruc¬ 
tor. The captain shall represent his party in get¬ 
ting assignments for the day's work. In selecting 
the members to constitute the various parties, sev¬ 
eral things should be kept in mind. Get in the same 
party men who will work well together, are punctual 
and want to work with the same degree of speed; 
place in the same party all the loafers, and men who 
are habitually late; place together in the same party 
all the athletes, as they usually leave early. If this 
is followed out, much of the discontent can be elimi¬ 
nated from the course, as in very few of the exer¬ 
cises can one or two men work alone. 

ABSENCES. 

When students are absent from the laboratory 
work, they will not be given credit for the work 
done by their party that day. There is just so much 
laboratory work to be done and when the student 
finishes that amount, he is done. Each student will 
be required to do the alloted amount. 

CARE OF SURVEYING EQUIPMENT. 

Each party will be provided with a key to a steel 
locker in the laboratory. A deposit of twenty-five 
cents will be required to insure the return of the 
key. In this locker will be found the following 
articles: Level, level rod, 100 foot tape, plumb bob, 
11 pins, 2 range poles, and a hatchet. Each party 
will be held responsible for the equipment in their 
locker. As two or more parties use the same locker, 
each party must return all the equipment to the 



8 


AGRICULTURAL SURVEYING LABORATORY 


locker each night. Any party may use the equip¬ 
ment on days that other parties are not assigned 
to use it. 

The level is a delicate instrument and should be 
handled with extreme care. Should you drop or in 
any way damage it, bring it immediately to the 
instructor. Should you try to use it after having 
damaged it, the results you obtain will be more than 
apt not to check. Under no condition take the instru¬ 
ment apart, as there are parts easily ruined by a 
slight breeze. Never set the instrument upon a con¬ 
crete floor and leave it, as the legs are liable to slip 
thus allowing the instrument to fall. Never go 
away and leave the level setting up in a field where 
there is stock as the stock are liable to damage it. 
In case of rain shield the level proper, either by 
placing it under your coat or some other way of 
providing cover for it. 

The level rod depends for its value on the painted 
lines and figures on its surface. Care should be ex¬ 
ercised to prevent these becoming scratched or in 
any way damaged. Do not throw the rod on the 
ground or do anything to scar its face. 

The range poles are fragile and if care is not 
taken of them they are liable to become broken. 
Their serviceability depends on the condition of their 
paint, so see that they are not unduly used. Do not 
attempt to spear chickens or vault ditches with 
them. 

The plumb bob should have its string coiled up 
each time it is put away and do not damage the 
point of the bob. 

The steel tape can be easily broken. Be careful 
in undoing it to see that no kinks are allowed to go 
unnoticed, as they will result in a broken tape. Do 
not allow teams or trains to run over them. After 
using the tape, it should be properly done up and 
tied securely. 

The hatchet and pins need to receive proper at¬ 
tention in order to be ready for another day. 



AGRICULTURAL SURVEYING LABORATORY 


9 


INVESTIGATING PACE 

Exercise 1 

Equipment.—Note book. 

Assignment.—Investigate length of pace: (a) 
Natural step, (b) Assumed three foot step. 

Instructions.—(a) Walk over the assigned course 
of 300 feet ten times, five times each way, walking 
as you naturally do. (b) Walk over the same course 
the same number of times, walking with an assumed 
step that you always thought was about three feet. 

Record all results in note book and compute aver¬ 
age length of natural step and assumed step. Throw 
out all values that vary more than two per cent. 

Specimen pages showing how notes should be 
written up will be found on pages 26 and 27. 


CHAINING DISTANCES 

Exercise 2 

Equipment.—100 foot tape, set of pins, two range 
poles and plumb bob. 

Assignment.—Chain distance both ways be¬ 
tween the two or more points assigned by the in¬ 
structor. Recording distance to the nearest .01 feet. 

Instructions.—Set the range poles at the points 
to be chained between. Head chainman takes all the 
pins, giving the rear chainman one pin. Rear chain- 
man should always line head chainman in. Between 
stations, rear chainman should drop chain and let it 
drag on the ground. Going up and down hills, be 
sure to use the plumb bob. Head chainman going 
one way, will be rear chainman returning. 

Record work neatly in note book. 





10 


AGRICULTURAL SURVEYING LABORATORY 


Two chainings should not differ more than one 
foot in 5,000 feet. 

Specimen pages showing how notes should be 
written will be found on pages 28 and 29. 


DETERMINING ANGLES WITH TAPE 

Exercise 3 

Equipment.—100 foot tape, set of pins and 2 
range poles. 

Assignment.—Determine the three angles in the 
triangle assigned by the instructor, using both 
methods on each angle (a). Sine Method; (b). Tan¬ 
gent Method. 

Instructions.—(a) Sine Method. Set range 
poles on the boundary lines of the angle to be 
measured. Measure from the vertex of the angle 
and along both boundary lines any number of feet, 
say 50 or 60. Be sure to measure the same 
number of feet on each boundary line. Place a pin 
at each of these points. Measure distances between 
these points to the nearest .01 of a foot. Half this 
distance divided by the distance measured out on 
the boundary line from the vertex of the angle will 
give the natural sine of half the angle. 

(b) Tangent Method.—Proceed as in (a) Sine 
Method. When distance between the two pins on 
boundary lines is obtained, locate half way point 
between these pins and then measure distance be¬ 
tween this half-way point and vertex of angle. This 
last distance divided into half the distance between 
the two points on boundary lines will give natural 
tangent of half the angle. 

Record all work in note book. 

Specimen pages showing how notes should be 
written will be found on pages 30 and 31. 




AGRICULTURAL SURVEYING LABORATORY 


11 


COMPUTING AREA OF TRIANGLE 

Exercise 4 

Equipment.—100 foot tape, two range poles and 
set of pins. 

Assignment.—Determine the area of the tri¬ 
angle by three different methods: (a) Three-side 
method, (b) Angle method, (c) Perpendicular 
method. 

Instructions.—Use same triangle assigned in 
Exercise 3. (a) Three-side method: Measure sides 
of triangle. Compute the area in square feet and in 
acres by use of the following formula: 

Area equals V s (s—a) (s—b) (s—c), 

a plus b plus c, equal 2S; 
a, b and c represent lengths of sides of tri¬ 
angle. 

(b) Angle method: Using angle values ob¬ 
tained in Exercise 3, compute area in square feet and 
in acres by use of the following^ formula: 

Area equals: One-half the product of two sides 
times the sine of the included angle. 

(c) Perpendicular method: Drop a line from 
the vertex of an angle through the base opposite the 
angle; having line perpendicular to base. Measure 
length of this line. Compute area in square feet and 
in acres by use of the following formula: 

Area equals: V 2 base times altitude. 

Record in your note book. 

Specimen pages showing how notes should be 
written up will be found on pages 32 and 33. 




12 


AGRICULTURAL SURVEYING LABORATORY 


LAYING OUT BUILDING 

Exercise 5 

Equipment.—100 foot tape, two range poles, set 
of pins and hatchet. 

Assignment.—Lay out building on a flat field, 
of the size and shape given by instructor, using 100 
foot steel tape. 

Instructions.—Direction of one side and location 
of one corner, together with diagram of building, 
will be obtained from instructor. Measure length of 
one side and erect at corners of this side per¬ 
pendiculars by using the 3, 4, 5 method. Measure 
length of these sides and set pins. You now have 
the four corners. Check by measuring diagonals; 
they should be equal. Any additional parts of the 
building can now be added in the same manner. 
Set stakes at the corners. 

When the entire building is staked out, call the 
instructor for approval. 

Record in your note book. 

Specimen pages showing how notes should be 
written will be found, on pages 34 and 35. 


DIFFERENTIAL LEVELING 

Exercise 6 

Equipment.—Level, level rod and hatchet. 

Assignment.—Determine the difference in eleva¬ 
tion between the two points assigned by the in¬ 
structor. 

Instructions.—The elevation of one of the points 
will be given by the instructor. Starting at that 
point, run a line of differential level over to the 
other assigned point, and when that point is reached, 
move the instrument, making a new set up and 




AGRICULTURAL SURVEYING LABORATORY 


13 


using the elevation obtained run another line of 
differentials back to the original starting point. 

Pay particular attention to the following points: 

Don’t take too long sights. 

Always hold the rod on a stake, concrete walk, 
railroad rail or some other substantial point. 

Have each man in party read rod in order to get 
practice and as a check. 

Assign each man in the party a definite job. 

The difference between the elevations taken at 
the start and that obtained after making the circuit 
should not be greater than .007 times the square 
root of the number of hundred feet the circuit in¬ 
cludes. 

Record all readings in note book as fast as they 
are made. 

Specimen pages showing how notes should be 
written will be found on pages 36 and 37. 


PROFILE LEVELING 

Exercise 7 

Equipment.—Level, level rod, hatchet and 100 
foot tape. 

Assignment.—Stake out, run profile levels and 
make profile for tile drain along line assigned by 
instructor. 

Instructions.—Starting at the outlet, place two 
stakes every 50 feet, 1% feet off line where tile is to 
be laid. One of these stakes is to be put down flush 
with the ground; the other is to show about one foot 
above the ground. Number stake at the outlet 
0—|—0, the next one 0—{—50, then 1—|—0, etc. 

Start at the B. M. and run a line of differential 
levels to one end or the other of the profile line, 
then take readings on top of profile stakes that are 




14 


AGRICULTURAL SURVEYING LABORATORY 


driven flush with top of ground. When the eleva¬ 
tion of the last station is obtained, run a line of dif¬ 
ferential levels back to the B. M. for a check. 

Plot up profile on standard Plate B profile paper. 

Locate a line of title on the profile, and deter¬ 
mine cut at each station. 

Record all notes in note book. 

Specimen pages showing how notes should be 
written up will be found on pages 38 and 39. 


READING ANGLES WITH INSTRUMENTS 

Exercise 8 

Equipment.—Level, plumb bob and two range 
poles. 

Assignment.—Using architect’s level, determine 
the size of each of three angles in the triangle 
assigned by the instructor. 

Instructions.—Place range poles on boundary 
lines of angle to be measured. Set the instrument 
up over the vertex of the angle, level instrument and 
sight on one range pole, get graduated circle to 
read zero. Sight on the other range pole and read 
angle. 

Instructor will give detail instructions as to how 
to read angles on graduated circles. 

Repeat for each angle. 

Record results in note book. 

Specimen pages showing how notes should be 
written up will be found on pages 40 and 41. 




AGRICULTURAL SURVEYING LABORATORY 


15 


TOPOGRAPHICAL SURVEYING 

Exercise No. 9 

Equipment.—Level, level rod, range poles, hatchet 
and 100 foot steel tape. 

Assignment.—Make a topographical survey of 
plot assigned by instructor. 

Instructions.—Measure length of sides and size 
of all angles. Divide the plot in 100 foot squares, 
placing a stake at each corner of the squares. Put 
station numbers on all stakes. Run line of differen¬ 
tial levels from bench mark to plot and establish 
temporary bench mark. Take the elevation of the 
ground at each stake to the nearest .1 foot. 

Locate all roads, fences, buildings and ditches. 

Make map of the plot, using a scale of one inch 
or decimal of an inch equals 100 feet, the scale being 
of such size to get a map that will conveniently fill a 
sheet of 18x24 drawing paper. Place contours on the 
map for every foot difference in elevation unless 
land is too rolling, then use two foot or five foot in¬ 
tervals. Plot in all roads, buildings, fences and 
ditches. 

Contour lines should be inked in as well as other 
things noted above. Elevations of points obtained 
should be noted with pencil on map. 

Record all notes taken in note book, using same 
form as used in profile leveling. 


DESIGNING DRAINAGE SYSTEMS 

Exercise 10 

Equipment.—Same as Exercise 9. 

Assignment.—Design the drainage system for 
the plot used in Exercise 9. 

Instructions.—Using map made in Exercise 9, 




16 


AGRICULTURAL SURVEYING LABORATORY 


design system of tile drainage, placing tile 80 feet 
apart and 30 inches deep. These lines of tile should 
be plotted on the map and inked in. When system is 
designed, take map to the instructor and he will 
select two lines of tile thereon. Stake these two 
lines out on the field and run profile levels over each. 
Plot up the profile, also the tile underneath it, 
having it at proper depth. Figure cuts for each sta¬ 
tion. 

Put length of tile lines and size of tile to be used 
on map. Make out bill of materials needed and give 
estimate of cost. 

Record all notes in note book. 


TILE INTERSECTION 

Exercise 11 

Equipment.—Tile spades, shovels, guage rod, 
string, ditch cleaner, hatchet and nails. 

Assignment.—Put in an intersection of a lateral 
and main tile drain. 

Instructions.—Using same two lines of tile that 
were staked out in Exercise 10. At intersection of 
two lines, put up string and dig ditch, smooth bot¬ 
tom and place four feet of tile on each line in the 
same as you would do in actual work. 

Call attention of the instructor when the work 
is done. 


TERRACING 

Exercise 12 

Equipment.—Home-made level, hatchet, farm 
level and rod. 

Assignment.—Using both methods, locate ter- 





AGRICULTURAL SURVEYING LABORATORY 


17 


races on the plot assigned by the instructor: (a) 
Using home-made level; (b) Using farm level. 

Instructions.—(a) Locate two terraces on as¬ 
signed hillside, using home-made level. Keep track 
of time it takes to run out terrace, together with 
length of terrace, (b) Locate two more terraces on 
the assigned hillside, using farm level. Keep track 
of time and length of terrace. 

In both cases, give terrace fall of six inches per 
hundred feet, and distance between terrace to be 
difference in elevation of six feet. 

Record data. 


LAYING OUT BUILDING 

Exercise 13 

Equipment.—Level, level rod, hatchet, 100 foot 
tape, pins and nails. 

Assignment.—Using architect’s level, lay out 
foundation and put up batter boards for building 
assigned by instructor. 

Instructions.—Instructor will furnish party with 
blue print of building to be used, assign a place to 
put the building and designate direction of one side 
and location of one corner. 

Lay off angles at corner of building with archi¬ 
tect’s level, measure sides with tape. Set stake with 
nail in top of it at each comer. Place batter boards 
two feet outside on each side of corner. Have top 
of boards level all around and at height of founda¬ 
tion. Place a nail in each board on line with side of 
buildings. 

Check diagonals of buildings. 

Record all in note book and draw diagram of 
building. 






18 


AGRICULTURAL SURVEYING LABORATORY 


ADJUSTMENT OF LEVEL 

Exercise 14 

Equipment.—Level, level rod and hatchet. 

Assignment.—Determine whether the level is out 
of adjustment. If it is, adjust it. 

Instructions.—Following the method outlined be¬ 
low in adjusting level. 

Record all work done in note book. 

In making the adjustment on any of the survey¬ 
ing instruments, first determine if it needs adjust¬ 
ment. If it does not, do not tamper with the instru¬ 
ment just for the sake of seeing how it is made. 
Many a good instrument or machine is often spoiled 
or thrown out of repair by its owner or user not be¬ 
ing able to leave well enough alone. When an instru¬ 
ment needs adjustment, go about making it with ex¬ 
treme care and caution. Surveying instruments are 
necessarily very delicate and should be so treated. 
In the wooden case that the instrument is kept, will 
be found the necessary pins, etc., to be used in ad¬ 
justing the instrument. Use them with care and do 
not use large amounts of force, as all adjusting 
screws should and will move easily when properly 
adjusted. Under no condition take the instrument 
apart. 


ADJUSTMENT OF WYE LEVEL 

The adjustment of the Wye level consists of four 
distinct adjustments. These should be taken up in 
the order that they are given. 

Adjustment of Cross Hairs.—This consists of get¬ 
ting the horizontal cross hairs horizontal and line 
of sight to coincide with centers of the pivot rings. 

To get the horizontal cross hair in a horizontol 
position, first level up the instrument and sight on 
some distant point, such as a pencil point on a 
brick wall. This point should rest on the horizontal 



AGRICULTURAL SURVEYING LABORATORY 


19 


cross hair. Next move the telescope so that it 
rotates around its vertical axis, the point should 
appear to move along the horizontal cross hair and 
traverse its entire length. If it does this, the cross 
hair is in adjustment, if it does not, the small cap¬ 
stan screws that hold the cross hairs should be 
loosened and the cross revolved until the above con¬ 
dition is satisfied, then the screws tightened. If 
there are more than one horizontal cross hair in the 
instrument, work with the middle one. 

To get the line of sight to coincide with the cen¬ 
ters of the pivot rings, have the instrument level as 
before and sight on some distant point that comes 
on the intersection of the two cross hairs. Then 
unclamp the telescope in the wyes and revolve the 
telescope 180° or so the bubble tube is above the 
telescope. If the intersection of the cross hairs re¬ 
mains on the point during this operation, the line 
of sight coincides with the center of the pivot rings. 
If it does not, then adjust the cross hairs by means 
of the capstan screws half the apparent error. Re¬ 
peat until correct. The horizontal cross hair can be 
moved up by loosening the lower capstan screw and 
tightening on the upper; it can be moved down by 
reversing the operation. The vertical cross hairs can 
be moved to the right or left by loosening the screw 
on the opposite side towards which it is to be moved, 
tightening on the other side. 

To Adjust the Axis of the Bubble Tube Parrallel 
to the Line of Sight.—There are two methods of do¬ 
ing this, the indirect and direct. While the indirect 
is quicker, it is not so accurate, and the direct or 
peg method will be given here. 

The peg adjustment is made by driving two 
stakes in the ground about 150 feet apart. Set the 
instrument up in front of one of these stakes so 
that when it is leveled up and a rod held on the 
stake, it will come within one-half or one-fourth 
inch of the end of the telescope. Make a reading on 



20 


AGRICULTURAL SURVEYING LABORATORY 


the rod at this point by turning the eye end of the 
telescope toward the rod and looking in the wrong 
end of the telescope. Place the point of a pen¬ 
cil on the rod to help in reading it. The cen¬ 
ter of the field of view is the place to put the point 
of the pencil, and the rod should be read at this 
point. (Fig. 1.) Let this instrument be set up at A, 



and this first rod reading be a. There sight on the 
rod held on B, this rod reading being b. Next move 
the instrument to the station B and make a reading 
on B which is called b'. Likewise a reading is made 
on A and is called a'. Now, if the instrument is in 
adjustment, the difference between a and b will 
equal the difference between a' and b', because these 
differences represent the difference in elevation be¬ 
tween the two stakes A. and B. However, if the 
differences are not equal, then the true difference 
in elevation will be equal to mean of the two differ¬ 
ences. This can be obtained by adding the two dif¬ 
ferences together and dividing by two. Then deter¬ 
mine by use of this true difference what the rod 
reading should be on A. (The instrument still being 
at B.) This can be done by determining the differ¬ 
ence between the a' and b' difference and the true 
difference and adding or subtracting to it the rod 
reading on a or a', in order to make the rod such an 
amount as to make the difference between it and b' 
equal to the true difference. Set the target on the 
rod to read this amount and bring the horizontal 
cross hair to read on the target by means of the 
leveling screws. Then bring the bubble to the cen- 















AGRICULTURAL SURVEYING LABORATORY 


21 


ter of the tube by means of the bubble adjustment 
screws at the end of the bubble. 

Repeat the entire operation until the level shows 
that it is in perfect adjustment. 

Example 

Instrument at A. 

Rod reading on A-a . . . 5.041 

Reading on B-b.3.291 

Difference.1.750 

Instrument at B. 

Reading on B-b' .... 4.219 
Reading on A-a' .... 7.029 

Difference.2.810 

Mean difference equals 1.750 plus 2.810 divided 
by 2, equals 2.280. The difference between 2.810 and 
2.280 is .530. The rod when held on A (the instru¬ 
ment still at B) should read 6.499—(7.029 minus 
.530)—in order to have the correct differences, be¬ 
cause the difference between b' and a' is greater 
than the true difference. 

Adjust the Axis of the Bubble Tube in the Same 
Plane With the Line of Sight.—Level the instru¬ 
ment, then clamp the telescope in the wyes and 
rotate the telescope in the wyes a very little; if the 
bubble remains in the center of the tube, it is in ad¬ 
justment. If it moves toward one end, then adjust 
by the azimuth screws, the ones that control the 
lateral movements of the bubble tube. Repeat until 
correct. 

To Adjust the Axis of the Bubble Tube Perpen¬ 
dicular to the Vertical Axis of the Instrument.— 
This adjustment is not absolutely necessary in order 








22 


AGRICULTURAL SURVEYING LABORATORY 


to get the correct readings, but is made as a mat¬ 
ter of convenience, as it insures that the instru¬ 
ment can be leveled so when turned in any direc¬ 
tion, it will remain level. To determine whether the 
level needs adjustment, first level it up over two 
screws and then over the other two, repeat two or 
three times. Then turn it through 180°; if it re¬ 
mains level, it is in adjustment. If, however, when 
turned the bubble moves toward one end or the 
other, it is out of adjustment. Proceed to correct 
half of the distance the bubble is out by means of 
the leveling screws, and the other half should be 
corrected by adjusting screws on the bottom of the 
wye. Repeat until in adjustment. 

Adjusting Dumpy Level.—The method used in 
adjusting a dumpy level is somewhat similar to the 
wye level, but the adjustments are taken up differ¬ 
ently and made at different points. Care should be 
taken to take its adjustments up in the order given. 
There are three adjustments to be made. 

Adjustment of Cross Hairs.—The horizontal 
cross hair should be horizontal, and the method 
used in determining its adjustment and making 
same is similar to the wye level which is given 
above. 

To Adjust the Axis of the Bubble Tube Perpen¬ 
dicular to the Vertical Axis of the Instrument.— 
The testing of the instrument to determine its ad¬ 
justment is the same as given for the wye level. 
To make the adjustment, half the correction is 
made with the leveling screws, the same as for the 
wye level, but the other half is made by the raising 
or lowering one end of the bubble tube instead of 
the wye, as on the wye level. 

To Adjust the Line of Sight Parallel to the Axis 
of the Bubble Tube.—The determining of the condi¬ 
tion of the level is the same as given for wye level. 
If out of adjustment, the proper reading is deter- 




AGRICULTURAL SURVEYING LABORATORY 


23 


mined as before given, but instead of bringing the 
instrument to read this reading by means of the 
leveling screws, the cross hairs are moved up or 
down until they read the proper place and the level¬ 
ing screws are not touched. 






SPECIMEN LABORATORY 

NOTES 




Kind of 
Pace 

Paces 

Total 

Average 

Natural 




1 

112.0 



2 

113.0 



3 

112.5 



4 

112.0 



5 

112.7 



6 

111.5 



7 

112.5 



8 

113.0 



9 

112.0 



10 

113.3 

1123.5 

112.35 

Assumec 

l 


* | 

1 

102.00 



2 

101.00 



3 

103.00 



4 

101.25 



5 

101.00 



6 

, 101.25 



7 

101.00 



8 

102.00 



9 

101.25 



10 

101.00 

1014.75 

101.48 




26 


Length 


2.66 


2.96 













INVESTIGATING PACE 

Exercise 1 


January 12, 1913. 


Length of Course 


Paul 


P. Jones. 
300 feet. 


2? 





Line 

Dir. 

Length 

Diff. 

Ratio 

A to B 

East 

3000.0 



B to A 

West 

3000.5 

0.5 

1:6000 






28 



















CHAINING DISTANCES 

Exercise 2 

January 15, 1913. 

Party. 

Paul P. Jones, Chainman. 

Sam S. Smith, Chainman. 

Roy R. West, Recorder. 

Point “A” was the southeast corner of the lower 
step at front of Agricultural Hall. Point “B” was 
the northeast corner of the lower step at front of 
Textile Building. 



29 


SINE METHOD 


Angle 

Hypo. 

V 2 Dist. 

Sine V 2 
Angle 

V 2 Ang. 

Angle 

ABC 

50 

26.25 

.5250 

31° 40' 

63° 20' 

BCA 

50 

25.94 

.5188 

31° 15' 

62° 30' 

CAB 

50 

22.81 

.4562 

27° 8' 

54° 16' 





Total, 

179° 76' 


TANGENT METHOD 


Angle 

Base 

V 2 Dist. 

Tan. Y 2 
Angle 

V 2 Ang. 

Angle 

ABC 

42.61 

26.25 

.6165 

31° 39' 

63° 18' 

BCA 

42.80 

25.94 

.6060 

31° 13' 

62° 26' 

CAB 

44.50 

22.81 

.5126 

27° 8' 

54° 16' 





Total, 

180° 00' 


. 


30 







DETERMINING ANGLES WITH TAPE 

Exercise 3 


January 16, 1913. 

Party. 

Paul P. Jones, Chainman. 

Roy R. West, Chainman. 

Sam S. Smith, Recorder. 

(Draw a diagram of the triangle you worked on, 
giving the letters you used.) 


31 



THREE SIDE METHOD 

Side 

Dist. 

Area 

Area 




Sq. ft. 

Acres 


a 

220.3 




b 

101.5 




c 

270.75 




S 

296.275 




S-a 

75.975 




S-c 

25.525 




S-b 

194.775 

10578.6 

.243 



A 

NGLE 

METHOD 

Side 

Dist. 

Area 

Area 




Sq. ft. 

Acres. 


a 

220.3 




b 

101.5 




Sin C. 

.9463 

10579.8 

.243 


: 

PERPENDICULAR METHOD 

Side 

Dist. 

Area 

Area 




Sq. ft. 

Acres 


c 

270.75 




Perp. 

78.2 

10586.3 

.243 




5 

2 

















COMPUTING AREA OF TRIANGLE 

Exercise 4 

January 17, 1913. 

Party. 

Roy R. West Chainman. 

Sam S. Smith, Chainman. 

Paul P. Jones, Recorder. 

(Draw a diagram of the triangle you worked 
on, giving the letters used.) 


33 




Line 

Length 

A-B 

200. 

A-C 

52. 

C-F 

25. 

D-E 

125. 

F-G 

10. 

G-H 

50. 

A-Z 

209.2 

B-Y 

209.3 

F-H 

50.98 

E-G 

50.95 






















LAYING OUT BUILDING 

Exercise 5 


January 18, 1913. 

Party. 

Paul P. Jones, Chainman. 

Sam S. Smith, Chainman. 

Roy R. West, Recorder. 

(Draw a diagram of the building you worked 
on; giving the letters you used.) 


Sta. 

B. M. 

- 1 - s 

H. I. 

— S 

Elev. 

100.00 


4.82 




1 

3.38 

104.82 

6.81 

98.01 

2 

3.445 

101.39 

8.51 

92.88 

3 

10.36 

96.325 

4.96 

91.365 

4 


101.725 

0.348 

101.377 


9.36 




5 

0.585 

110.737 

0.59 

110.147 

6 

0.495 

110.732 

9.24 

101.492 

n 

l 

4.71 

101.987 

10.29 

91.697 

8 

8.525 

96.407 

3.425 

92.982 

9 

7.77 

101.507 

4.43 

97.077 

10 


104.847 

4.84 

100.007 

Check 

53.450 


53.443 



53.443 



100.007 

• 

.007 



100.000 





.007 



31 

J 































DIFFERENTIAL LEVELING 

Exercise 6 


January 20, 1913. 

Party. 

Paul P. Jones, Levelman. 

Roy R. West, Rodman. 

Sam S. Smith, Recorder. 

B. M. is a cross on the southeast corner of the 
lower stone step in front of Agricultural Hall. Sta¬ 
tion 5 was the northwest corner of lower stone 
step in front of Textile Building. 


37 


Sta. 

B. M. 

-|- S. 

H. I. 

— S 

Elev. 

100 


1.70 

101.70 



0-|-0 



5.43 

96.27 

0-|-50 



7.96 

93.74 

l-l-o 



6.30 

95.40 

1-1-50 



4.46 

97.24 

to 

1 

1 

o 



3.25 

98.44 

2-|-50 



1.63 

100.07 

2-|-86 

3.40 

103.40 

1.70 

100.00 

B. M. 



3.39 

100.01 


8 


G. L. 

89.40 
91.20 
92.80 

94.40 
96.00 
97.50 
98.00 




PROFILE LEVELING 

Exercise 7 

January 21, 1913. 

Cut. 

6.87 

2.54 

2.60 

2.80 

2.44 

2.57 

2.00 

Party. 

Sam S. Smith, Levelman. 

Roy R. West, Rodman. 

Paul P. Jones, Recorder. 

B. M.—Nail on south side of hickory tree, ten 
feet north of foot bridge. 


39 


Angle. Degrees. 


Min. 


ABC ' 61 
BCA 90 
CAB 27 


32 

51 

40 


Total 180 
























READING ANGLES WITH INSTRUMENT 

Exercise 8 

January 22, 1913. 

Party. 

Paul P. Jones, Instrumentman. 

Roy R. West, Rodman. 

Sam S. Smith, Rodman. 

(Draw a diagram of the triangle you worked on 
giving the letters used.) 


41 





























































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































i 









































































































































• 



s 

























































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































AGRICULTURAL SURVEYING LABORATORY 


73 


SURVEYING WITH STEEL TAPE 


Determining the Size of a Given Angle. 

Sine Method.—Refer to Fig. 2. Let angle BAC 
be the angle to be measured. Set the range poles at 
B and C with the tape measure out from A on line 
AB some even distance, say 40, 50, 60, 80 or 100 
feet. Locate this point as D with a chain pin. Do 



the same thing on line AC, using the same distance, 
and thus locate point E; mark with a chain pin. 
Now find the exact distance between D and E in feet 
and tenths of a foot. The size of angle BAC can 
now be found by the following computations. Take 
half the distance DE; divide it by the distance AD; 
look this value up in the table of natural sines and 
find the angle it represents. Twice this angle will be 
the angle BAC. 

Proof.—AF divides the angle BAC into equal 
parts and AFD is a right angle. Why? Let the 
angle BAC be represented by X. Then sine X/2 
equals DF over AD. Determine what X/2 is and 
twice that would be X. 

Caution.—Don’t multiply sine X/2 by 2 and then 
look up value of angle and expect to get X. 

Large Angles.—Should the angle that is to be 
measured be greater than 90°, it would be better 
to measure the angle that is less than 180° or in 
some cases 360°. In Fig. 3 is shown a case when 






74 AGRICULTURAL SURVEYING LABORATORY 


instead of measuring the angle BAC it would be 
better to extend the line AC to some point G and 
measure the angle GAB. When GAB is found, sub¬ 
tract it from 180° and this will give CAB. 



Fig. 3. 


Tangent Method.—First Method: Refer to Fig. 
4. Let angle CAB be the angle to be measured. Set 
range poles up at B and C. Measure some even dis¬ 
tance, 40, 50, 60 or 100 feet out on line AC from 
A. Let this point be E. Erect a right angle at E 
on line AC. Find where the line perpendicular to 
AC and through E intersects AB and let that point 
be D. Measure the length of DE. Now, the angle 
BAC can be found by the following computations. 
Divide the length of DE by the length AE, and 



Fig. 4. 


with the result find what angle it is the natural 
tangent of. This angle is BAC. 

Proof.—Natural tangent of BAC equals DE over 
AE. 

Second Method.—Refer to Fig. 2. Proceed the 
same as was done in Sine Method and get the lengths 
of AE and AD also DE. Then located F on the ground 
and mark it with a chain pin. Measure AF, getting 
its length in feet and tenth of a foot. Now, the angle 
can be obtained by the following computations: 







AGRICULTURAL SURVEYING LABORATORY 


75 


Divide length of DF by the length AF. Find what 
angle this value is the natural tangent of. Twice 
this angle will be angle BAC. 

Choice of Method.—The first method can be used 
on small angles, while the second is better for 
larger angles. When a check is wanted, the second 
method is best, as the sine method can be also 
worked for the value obtained. 

Large Angles.—The same remarks given under 
Sine Method, regarding the obtaining of values of 
angles approaching or greater than 180°, also apply 
here. 

Practical Applications.—The ability to determine 
the size of an angle in the fence corner of a field 
by means of a tape will often be found useful in 
farm life. Then, too, other occasions may arise 
when it is necessary to determine some angle and 
no instrument is at hand. 


LAYING OFF A GIVEN ANGLE 

Right Angles. 

Three-Four-Five Method.—Refer to Fig. 5. Let 
line AB be the line that the right angle is to be laid 



off on, and point C to be the point on that line the 
angle is made. Have one man hold the 0 end of the 
tape and the 60 foot mark at this point C. Have 
another man to hold the 40 foot mark on the line 






76 


AGRICULTURAL SURVEYING LABORATORY 


AB. The third man can sight him from point A, 
so he will be on line. This man at E, then will be 
20 feet from C. The third man then takes the 15-foot 
mark and goes to some point D, which will be 
found when the tape is pulled tight along line DE 
and DC. Then a line through CD is perpendicular 
to AB and the angle ACF is a right angle. 

Proof.—20 squared, plus 15 squared, equals 25 
squared. This is called the three-four-five method, 
because any multiples of three, four and five can 
be used. 

Chord Method. 

First Method.—Refer to Fig. 6. Let line AB be 
a straight line and C be the point on that line at 
which a right angle is wanted. Set up range poles 
at A and B. Measure off some distance from C and 
locate any point D on line AB; then measure off 
the same distance on the other side of C and locate 
point E on line AB. Using the steel tape, take a 


A- 


D 



Fig. 6. 



radius somewhat greater than EC, and with E as a 
center describe, with a chain pin, an arc. With the 
same radius and D as a center, describe another arc. 
Those two arcs will intersect at some point F. A 
line through C and F will be perpendicular to AB 
and ACF, as well as BCF will be right angle. Why? 

Second Method.—Refer to Fig. 7. Let AB be a 
straight line and point C be some point off AB, 
through which a line perpendicular to AB is wished 
to be passed. Set up range poles at A and B. With 







AGRICULTURAL SURVEYING LABORATORY 


77 


the steel tape one end at C as a center and a radius 
greater than CF, describe an arc with a chain pin 



Fig. 7. 


which will cut the line AB at two points D and E. 
A man standing at A can sight along AB and tell 
when pin intersects this line. Find half the distance 
between D and E, which will be some point F. A line 
through F and C will be perpendicular to AB and 
the angles AFC and BFC will be right angles. Why? 

Semicircle Method.—Refer to Fig. 8. Let line 
AB be a straight line and point C will be some point 
on that line at which a right angle is to be erected. 
Set range poles up at A and B. Take some point 


vE 



Fig. 8. 

F off the line AB. With one end of the steel tape 
at F and a raidus FC, describe a semicircle which 
at one end, shall cut AB at some point D. Pass a 
line through DF until it intersects the semcircle at 
some point E. A man at D can sight through F, 
and locate a pin held on the semicircle. Then a line 
passed through C and E is perpendicular to AB and 
the angles ACE and BCE are right angles. Why? 










78 


AGRICULTURAL SURVEYING LABORATORY 


ANGLES OTHER THAN A RIGHT 

ANGLE 


Sine Method.—To use this method, do what you 
did to lay out an angle with Sine Method, only do it 
backwards. That is, divide the angle you wish to lay 
out by 2, find the natural sine of that angle. Refer 
to Fig. 2. Select the lengths AD and AE. Multiply 
this distance by the sine of the angle and the result 
will be DF or EF. Twice the distance will be DE. 
Now, with a pin set at A, the point at which you 
wish the angle made, measure out on AC or AB, 
the direction of one of the lines must be given, the 
distance you selected. Set a pin at this point. Say it 
is E. Then, with the zero end of the tape at A, and one 
man holding on the number of feet equal to ADE or 
AE plus DE, and stationed at E, let another man 
holding on the number of feet on the tape equal to 
AD or AE draw the tape so it is tight on E, and 
on A the point at which he finds himself, will be 
D. Place a pin here and the given angle is laid out. 
Prove it. 

Tangent Method.—This can be done by working 
the tangent method of laying out angles backwards. 
The student should be able to figure this out him¬ 
self after having studied the method given above. 

Practical Applications.—The ability to lay off all 
kinds of angles with the tape alone will be found 
very useful, particularly in the case of the right 
angle, as it can be used at many different times on 
the farm. 

The laying out of a building site is a very fre¬ 
quent necessity on the farm. When it is desired to 
have the building “square with the world,” and noth¬ 
ing near is in that condition, to which the building can 
be made parallel with, it will be necessary to have 
an instrument. But under all other conditions, the 




AGRICULTURAL SURVEYING LABORATORY 


79 


site can be easily and quickly laid off with noth¬ 
ing but a tape. Suppose it was wished to lay 
off a building of the size and shape shown in Fig. 
9. Suppose one side, AB was given, and the corner 
D located; then C could be located by measuring 



Fig. 9. 


100 feet from D on line AB. Next, erect a per¬ 
pendicular by the 3-4-5 method at the points C. 
and D. Measure upon these perpendiculars 50 feet 
and set pins which will locate points E and F. 
Now, measure the diagonals DF and CE on this rect¬ 
angle. If they are equal, this part of the building is 
all right. Then measure on line EF 20 feet from E; 
this will locate J; 20 feet further along this line 
will locate I. Erect perpendiculars at I and J and 
measure up 10 feet on each line, which will locate 
G and H. Measure the diagonals GJ and IH. If 
equal, this part of the building is all right. The 
building is now laid out as all the corners are 
located. No matter how complicated a building may 
be, it can be laid out with this method, if it is first 
divided into square and rectangles. 

Parallel Lines*—One line parallel to another 
can be laid off as mentioned above in laying off a 
building. They should be checked the same way. 









80 


AGRICULTURAL SURVEYING LABORATORY 


TABLE OF AREAS DRAINED BY TILE 


The following table gives the number of acres 
that different tile will drain with the various grades 
or falls. To look up the size of tile needed to drain a 
certain number of acres with a given fall, look up 
the fall or grade in the left hand column and then 
move to the right along the horizontal column oppo¬ 
site this grade until the number of acres is found. 
Then go vertically along this column and the size of 
tile will be found. 

Suppose 36 acres is to be drained with a fall of 
.2 feet per 100 feet. Come down the left-hand col¬ 
umn until .2 is found, then go to the right until 
36 is found, and this number 36 is found in the 
same vertical column, as 10-inch tile. Therefore, 
a ten-inch tile is to be used. 

Areas Drained by Tile Mains Where One-Half of 
Water is Removed in Twenty-Four Hours. 


(Based on Kutter’s Formula Where "N” equals .015.) 


Fall Per 
100 Ft. 

4 

5 

6 

Diameter of Tile in Inches 

7 8 10 12 15 

18 

24 

.05 

1 

o 

lu 

4 

6 

9 

17 

29 

52 

87 

190 

.06 

1 

2 

5 

7 

10 

19 

32 

57 

97 

208 

.07 

1 

2 

5 

7 

11 

21 

35 

62 

105 

226 

.08 

2 

3 

5 

8 

12 

23 

38 

67 

112 

244 

.09 

2 

3 

6 

9 

13 

24 

41 

72 

119 

262 

.10 

2 

3 

6 

9 

14 

26 

43 

76 

126 

280 

.12 

2 

3 

6 

9 

14 

27 

46 

82 

137 

310 

.14 

2 

3 

6 

10 

16 

29 

49 

89 

146 

354 

.16 

2 

4 

7 

11 

17 

31 

53 

96 

156 

358 

.18 

2 

4 

7 

12 

18 

33 

56 

104 

166 

377 

.20 

2 

5 

8 

13 

20 

36 

59 

108 

176 

396 

.25 

2 

5 

9 

14 

21 

39 

66 

120 

198 

440 

.30 

3 

6 

10 

16 

24 

44 

73 

132 

216 

487 

.40 

4 

7 

12 

18 

28 

50 

85 

155 

251 

565 

.50 

4 

8 

13 

21 

30 

56 

95 

174 

281 

628 




AGRICULTURAL SURVEYING LABORATORY 


81 


FalljPer Diameter of Tile in Inches 


;ioo Ft. 

4 

5 

6 

7 

8 

10 

12 

15 

18 

.60 

5 

9 

15 

23 

33 

62 

104 

189 

309 

.70 

5 

9 

16 

25 

36 

67 

112 

203 

333 

.80 

5 

10 

17 

27 

39 

72 

120 

217 

356 

.90 

6 

11 

18 

28 

41 

76 

127 

230 

380 

1.00 

6 

11 

19 

29 

43 

80 

134 

244 

400 

1.25 

7 

12 

21 

33 

48 

90 

150 

271 


1.50 

7 

14 

24 

36 

53 

98 

165 



1.75 

8 

15 

25 

39 

57 

105 

172 



2.00 

9 

16 

27 

42 

61 

113 

189 



3.00 

10 

20 

33 

51 

75 

139 





TILE DRAINAGE ESTIMATING 

Preliminary Estimate of Cost.—It is often neces¬ 
sary to make a preliminary estimate of the cost be¬ 
fore any surveying has been done in order to give 
an approximate cost of the drainage. The following 
figures given by Elliott will be of assistance in this 
work. 

The number of tile needed for laterals to drain 
an acre of ground with different spacings: 


20 feet apart, 2178 feet per acre. 


25 “ 

u 

1742 

« 

a 

a 

30 “ 

« 

1452 

u 

a 

u 

33 “ 

M 

1320 

it 

<< 

« 

40 “ 

« 

1089 

it 

a 

(« 

50 “ 

«( 

872 

li 

<( 

« 

66 “ 

« 

660 

it 

it 

«{ 

80 “ 

a 

545 

i( 

<( 

« 

100 “ 

tt 

436 

ti 

<( 

«( 

150 “ 


291 

it 

<< 

(( 

200 “ 

‘t 

218 

<< 

u 

« 


The number of feet of mains is not included in 
this table and must be added. 









82 


AGRICULTURAL SURVEYING LABORATORY 


Bill of Materials.—After the survey has been 
made and the tile lines plotted up on the map, a bill 
of materials should be made out. This bill should 
contain the number of feet of each size of tile 
needed. The actual number of feet needed should be 
increased 10% in order to allow for breakage. The 
number of tile specials and materials for accessories 
should all be included. 

Estimating Cost.—The bill of material will serve 
as a basis for estimating cost of installing the tile 
drainage. The cost can be divided into five parts: 
cost of tile, cost of hauling, cost of installing tile, 
cost of accessories, and cost of engineering and 
superintendence. 

Cost of Tile.—The cost of tile varies with dif¬ 
ferent states and parts of the state. They are quoted 
in lots of 1,000 feet. The following prices are about 
the average carload lot prices, delivered at the 
farmer’s railroad station, in Mississippi: 

MISSISSIPPI DRAIN TILE PRICE PER 1,000 

FEET 

4 inch tile, $ 16.00 per 1,000 feet. 


5 

ii 

ii 

24.00 

ii 

ii 

a 

6 

ii 

ii 

30.00 

ii 

ii 

a 

7 

a 

ii 

40.00 

ii 

ii 

a 

8 

ii 

ii 

55.00 

ii 

a 

a 

10 

ii 

ii 

75.00 

ii 

a 

a 

12 

ii 

ii 

110.00 

ii 

a 

a 

14 

ii 

ii 

175.00 

ii 

a 

a 

16 

ii 

ii 

220.00 

ii 

a 

a 

18 

ii 

ii 

300.00 

ii 

a 

a 

20 

ii 

ii 

385.00 

ii 

a 

a 

22 

ii 

ii 

460.00 

ii 

a 

a 

24 

ii 

ii 

520.00 

ii 

a 

a 


Cost of Hauling.—The cost of hauling the tile 
from the railroad station to the farm should be 








AGRICULTURAL SURVEYING LABORATORY 


83 


estimated. In order to determine this, it is neces¬ 
sary to know the weight of various sizes of tile. 
The following table, given from Elliott’s Practical 
Farm Drainage, will give this information. 


WEIGHT OF CLAY DRAIN TILE 


Size in 

Weight per Ft. Average Carload 

No. of Feet 

Inches 

in Lbs. 

in Feet 

per Ton 

4 

6 

6500 

334 

5 

8 

5000 

250 

6 

11 

4000 

182 

7 

14 

3000 

143 

8 

18 

2400 

111 

10 

25 

1600 

80 

12 

33 

1000 

60 

14 

43 

800 

56 

16 

53 

500 

38 

18 

70 

400 

27 

20 

83 

332 

24 

22 

100 

320 

20 

24 

112 

300 

18 

The number of tons 

of tile to be hauled should 

be determined 

and the 

distance in miles. 

Then the 

following table of cost 

of hauling will 

enable the 

total cost to be computed. This table is 
from Elliott’s Practical Farm Drainage. 

also taken 


COST OF HAULING 


Hauling, one mile, 
Hauling, two miles, 
Hauling, three miles, 
Hauling, four miles, 
Hauling, five miles, 


$ .65 per ton. 
.80 per ton. 
1.15 per ton. 
1.35 per ton. 
1.60 per ton. 


This table of cost is with the road in fair condi¬ 
tion and allowing the team and driver $3.50 per day. 


Cost of Installing Tile.—This cost can be divided 
into two parts, cost of digging and laying, which 






84 


AGRICULTURAL SURVEYING LABORATORY 


consists of excavating the ditch, laying the tile and 
placing enough dirt on top of the tile to keep it 
from moving. Where the farmer does his own work, 
this is the way it can be figured, or where the ditch 
is dug by a machine, they usually do not care to take 
the contract for refilling the ditch. However, where 
the work is done by some contractors, they will con¬ 
tract for the entire work. 

The prices given below are by a tile contractor 
who has done considerable work near Tupelo, Miss. 
They are prices for the work complete, digging 
ditch, laying tile and filling ditch again. 

TILE PRICES 

Prices for Tile Laying Complete as furnished by 
Lee Brewster, Baldwyn, Miss.j December 18, 1913. 
Cost in cents per inch of depth for one rod. 


DEPTH IN INCHES 


Size of Tile 

48 in. 

or Less 

48 in. 

to 60 in. 

60 in. 

to 96 in. 

4" 

1 

cents 

1% 

cents 



5" 

1 

ii 

1% 

<< 



6" 

l 1 /,i 

a 

iy 2 

u 



00 

1V2 

a 

1 % 

u 

2 

cents 

10" 

2 

a 

2y 4 

il 

2y 2 

a 

12" 

2% 

a 

2y 2 

u 

2 % 

ii 

15" 



3 

li 

3 % 

a 

18" 



3y 2 

t( 

4 

ii 


Machine ditching and laying costs about 25 
cents per rod for 4 to 6 inch tile laid 3 feet deep. 
This includes digging, laying and putting in just 
enough to hold the tile in place. 

The cost of filling the ditch is as follows: 

Filling ditch 3 ft. deep, by hand, 6 cents per rod. 

Filling ditch 3 ft. deep, scraper or plow, 3 cents 
per rod. 

The above is for up to 6 inch tile. 

Deeper and wider ditches in proportion. 








AGRICULTURAL SURVEYING LABORATORY 


85 


Cost of Accessories.—The cost of accessories 
should be figured from the materials and labor 
needed. The amount of brick, cement, sand, gravel, 
etc., should all be made out and cost figured at 
market prices. 

Cost of Engineering and Superintendence.— 
Where the farmer is able to do this himself, it need 
not be taken into account, but in cases where it is 
to be taken into account, it usually runs about five 
per cent of the total cost. 



86 


AGRICULTURAL SURVEYING LABORATORY 


COMPUTING AREAS 

Area of a Square.—The area of a square is the 
square of one of its sides. 

Area of Parallelogram.—A parallelogram is a 
figure with four straight sides, the opposite sides 



of which are parallel. (Fig. 10.) The area of this 
figure is equal to the base times the altitude. 



b -I- c 

Area - - - x a 

2 


Area of a Trapezoid.—A trapezoid is a figure 
having four straight sides only two of which are 
parallel. (Fig. 11.) The area of this figure is equal 
to the altitude times the mean length of the parallel 
sides. 
















AGRICULTURAL SURVEYING LABORATORY 


87 


Area of a Triangle.—First, base and altitude 



Fig. 12. 


2 

given. The area of a triangle is equal to one-half 
the base times the altitude. (Fig. 12.) 

Second, three sides given. Let the sum of the 
sides of a triangle be equal to two times s, then 
apply the formula given in Fig. 13. 



Fig. is. 

a -|- b —|—c equal 2s 
Area equals Vs (s-a) (s-b) (s-c) 

Third, two sides and the included angle given. 
The area of a triangle is equal to one-half the prod¬ 
uct obtained by multiplying the two sides together 
and then multiplying the result by the sine of the 
included angle. (Fig. 14.) 
















AGRICULTURAL SURVEYING LABORATORY 


88 



Area of a Trapezium.—A trapezium is a figure 
having four straight lines, no two sizes of which are 
parallel. Divide the trapezium into two triangles 
and determine the area of each triangle, then add 



Fig. 15. 

Area triangle 1 equals %ab sine F. 

Area triangle 2 equals %cd sine E. 

Area trapezium equals area 1—1—2. 

the two areas together. In Fig. 15 this is shown 
when the length of four sides and the size of two 
of the angles are given. 

Area of a Many-Sided Figure.—In obtaining the 
area of a many-sided figure it is best, if possible, 
to resolve it into a number of triangles and then 
measure the sides of the triangles. 










AGRICULTURAL SURVEYING LABORATORY 


89 


TABLES OF MEASUREMENT 


Linear Measure 

(United States.) 

12 inches equal 1 foot. 

3 feet equal 1 yard. 

1 6 V 2 feet equal 1 rod. 

320 rods equal one mile. 

5280 feet equal one mile. 

1760 yards equal 1 mile. 

Metric. 

10 millimeters equal 1 centimeter. 
10 centimeters equal 1 decimeter. 
10 decimeters equal 1 meter. 

1000 meters equal 1 kilometer. 

Gunters Chain. 

1 chain equals 100 links. 

1 chain equals 4 rods. 

80 chains equal 1 mile. 

Conversion Table 

1 chain equals 66 feet. 

1 chain equals 20.1168 meters. 

1 link equals 7.92 inches. 

1 link equals 0.66 feet. 

1 foot equals 0.3048 meters. 

1 inch equals 2.54 centimeters. 

1 meter equals 3.28023 feet. 

1 centimeter equals .3937 inches. 




90 


AGRICULTURAL SURVEYING LABORATORY 


Conversion Table 

To Change Tenths and Hundredths of a Foot to Inches. 



.00 

.01 

1 .02 

.03 

| .04 

.05 

.06 

1 .07 

.08 

1 - 09 Jl 

0 

0 

% 

% 

% 

% 

% 

% 

% 

1 

1% 

0 

.1 

1 % 

1 % 

i % 

1 % 

i % 

1 % 

1 % 

2 

2 % 

2 % 

.1 

.2 

2 % 

2 % 

2 % 

2 % 

2 % 

3 

3 % 

3 % 

3 % 

3 % 

.2 

.3 

3 % 

3 % 

3 % 

4 

4 % 

4 % 

4 % 

4 % 

4 % 

4 % 

.3 

.4 

4 % 

5 

5 

5 % 

5 y 4 

5 % 

5 % 

5 % 

5 % 

5 % 

.4 

.5 

6 

6 % 

e % 

6 % 

6 % 

6 % 

6 % 

6 % 

7 

7 % 

.5 

.6 

7 % 

7 % 

7 y 2 

7 % 

7 % 

7% 

7 % 

8 

8 % 

8 % 

.6 

.7 

8 % 

s % 

8 % 

8 % 

8 % 

9 

9 % 

9 % 

9 % 

9 % 

.7 

.8 

9 % 

9 % 

9 % 

10 

10 % 

10 % 

10 % 

10 % 

10 % 

10 % 

.8 

.9 

10 % 

11 

11 

11 % 

11 % 

11%|11%|11%|U%|11%| .9 

1 1 I 1 1 


Surface Measure. 

United States. 

144 sq. in equal 1 sq. ft. 

9 sq. ft. equals 1 sq. yd. 

30% sq. yd. equal 1 sq. rd. 

272 % sq. ft. or 43560 sq ft. or 160 sq. rods equal 
1 acre. 


Metric 

100 sq. millimeters equal 1 sq. cen. 

1000 sq. centimeters equal 1 sq. decim. 
1 sq. meter equals 10.7639 sq. feet. 
10000 sq. metors equals 1 hectaro. 

Conversion Table 

10 sq. chains equals 1 acre. 

1 acre equals 4046.87 sq. meters. 

1 sq. meter equals 10.7369 sq. feet. 

1 hectare equals 2.47104 acres. 





















AGRICULTURAL SURVEYING LABORATORY 


91 


LOGARITHMS OF NUMBERS 

FROM 0 TO 1000 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

°! 

00000 

30103 

47712 

60206 

69897 

77815 

845H) 190309 

95424 

10 

00000 

00432 

00860 

01284 

01703 

02119 

02531 

02938 

03342 

03743 

11 

04139 

04532 

04922 

05308 

05690 

06070 

06446 

06819 

07188 

07555 

12 

07918 

08279 

08636 

08991 

09342 

09691 

10037 

10380 

10721 

11059 

13 

11394 

11727 

12057 

12385 

12710 

13033 

13354 

13672 

13988 

14301 

14 

14613 

14922 

15229 

15534 

15836 

16137 

16435 

16732 

17026 

17319 

15 

17609 

17898 

18184 

18469 

18752 

19033 

19312 

19590 

19866 

20140 

16 

20412 

20683 

20952 

21219 

21484 

21748 

22011 

22272 

22531 

22789 

17 

23045 

23300 

23553 

23805 

24055 

24304 

24551 

24797 

25042 

25285 

18 

25527 

25768 

26007 

26245 

26482 

26717 

26951 

27184 

27416 

27646 

19 

27875 

28103 

28330 

28556 

28780 

29003 

29226 

29447 

29667 

29885 

20 

30103 

30320 

30535 

30750 

30963 

31175 

31387 

31597 

31806 

32015 

21 

32222 

32428 

32634 

32838 

33041 

33244 

33445 

33646 

33846 

34044 

22 

34242 

34439 

34635 

34830 

35025 

35218 

35411 

35603 

35793 

35984 

23 

36173 

36361 

36549 

36736 

36922 

37107 

37291 

37475 

37658 

37840 

24 

38021 

38202 

38382 

38561 

38739 

38917 

39094 

39270 

39445 

39620 

25 

39794 

39967 

40140 

40312 

40483 

40654 

40824 

40993 

41162 

41330 

26 

41497 

41664 

41830 

41996 

42160 

42325 

42488 

42651 

42813 

42975 

27 

43136 

43297 

43457 

43616 

43775 

43933 

44091 

44248 

44404 

44560 

28 

44716 

44871 

45025 

45179 

45332 

45484 

45637 

45788 

45939 

46090 

29 

46240 

46389 

46538 

46687 

46835 

46982 

47129 

47276 

47422 

47567 

30 

47712 

47857 

48001 

48144 

48287 

48430 

48572 

48714 

48855 

48996 

31 

49136 

49276 

49415 

49554 

49693 

49831 

49969 

50106 

50243 

50379 

32 

50515 

50651 

50786 

50920 

51055 

51188 

51322 

51455 

51587 

51720 

33 

51851 

51983 

52114 

52244 

52375 

52504 

52633 

52763 

52892 

53020 

34 

53148 

53275 

53403 

53529 

53656 

53782 

53908 

54033 

54158 

54283 

35 

54407 

54531 

54654 

54777 

54900 

55023 

55145 

55267 

55388 

55509 

36 

55630 

55751 

55871 

55991 

56110 

56229 

56348 

56467 

56585 

56703 

37 

56820 

56937 

57054 

57171 

57287 

57403 

57519 

57634 

57749 

57864 

38 

57978 

58093 

58206 

58320 

58433 

58546 

58659 

58771 

58883 

58995 

39 

59106 

59218 

59329 

59439 

59550 

59660 

59770 

59879 

59988 

60097 

40 

60206 

60314 

60423 

60531 

60638 

60746 

60853 

60959 

61066 

61172 

41 

61278 

61384 

61490 

61595 

61700 

61805 

61909 

62014 

62118 

62221 

42 

62325 

62428 

62531 

62634 

62737 

62839 

62941 

63043 

63144 

63246 

43 

63347 

63448 

63548 

63649 

63749 

63849 

63949 

64048 

64147 

64246 

44 

64345 

64444 

64542 

64640 

164738 

64836 

64933 

65031 

65128 

65225 
































92 


AGRICULTURAL SURVEYING LABORATORY 


LOGARITHMS OF NUMBERS, FROM 0 TO 1000. 


( Continued. ) 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

45 

65321 

65418 

65514 

65610 

65706 

65801 

65896 

65992 

66087 

66181 

46 

66276 

66870 

66464 

66558 

66652 

66745 

66839 

66932 

67025 

67117 

47 

67210 

67302 

67394 

67486 

67578 

67669 

67761 

67852 

67943 

68034 

48 

68124 

68215 

68305 

68395 

68485 

68574 

68664 

68753 

68842 

68931 

49 

69020 

69108 

69197 

69285 

69373 

69461 

69548 

69636 

69723 

69810 

50 

69897 

69984 

70070 

70157 

70243 

70329 

70415 

70501 

70586 

70672 

61 

70757 

70842 

70927 

71012 

71096 

71181 

71265 

71349 

71433 

71517 

52 

71600 

71684 

71767 

71850 

71933 

72016 

72099 

72181 

72263 

72346 

63 

72428 

72509 

72591 

72673 

72754 

72835 

72916 

72997 

73078 

73159 

54 

73239 

73320 

73400 

73480 

73560 

73640 

73719 

73799 

73878 

73957 

55 

74036 

74115 

74194 

74273 

74351 

74429 

74507 

74586 

74663 

74741 

56 

74819 

74896 

74974 

75051 

75128 

75205 

75282 

75358 

75435 

75511 

57 

75587 

75664 

75740 

75815 

75891 

75967 

76042 

76118 

76193 

76268 

58 

76343 

76418 

76492 

76567 

76641 

76716 

76790 

76864 

76938 

77012 

59 

77085 

77159 

77232 

77305 

77379 

77452 

77525 

77597 

77670 

77743 

60 

77815 

77887 

77960 

78032 

78104 

78176 

78247 

78319 

78390 

78462 

61 

78533 

78604 

78675 

78746 

78817 

78888 

78958 

79029 

79099 

79169 

62 

79239 

79309 

79379 

79449 

79518 

79588 

79657 

79727 

79796 

79865 

63 

79934 

80003 

80072 

80140 

80209 

80277 

80346 

80414 

80482 

80550 

64 

80618 

80686 

80754 

80821 

80889 

80956 

81023 

81090 

81158 

81224 

65 

81291 

81358 

81425 

81491 

81558 

81624 

81690 

81756 

81823 

81889 

66 

81954 

82020 

82086 

82151 

82217 

82282 

82347 

82413 

82478 

82543 

67 

82607 

82672 

82737 

82802 

82866 

82930 

82995 

83059 

83123 

83187 

68 

83251 

83315 

83378 

83442 

83506 

83569 

83632 

83696 

83759 

83822 

69 

83885 

83948 

84011 

84073 

84136 

84198 

84261 

84323 

84386 

84448 

70 

84510 

84572 

84634 

84696 

84757 

84819 

84880 

84942 

85003 

85065 

71 

85126 

85187 

85248 

85309 

85370 

85431 

85491 

85552 

85612 

85673 

72 

85733 

85794 

85854 

85914 

85974 

86034 

86094 

86153 

86213 

86273 

73 

86332 

86392 

86451 

86510 

86570 

86629 

86688 

86747 

86806 

86864 

74 

86923 

86982 

87040 

87099 

87157 

87216 

87274 

87332 

87390 

87448 

75 

87506 

87564 

87622 

87680 

87737 

87795 

87852 

87910 

87967 

88024 

76 

88081 

88138 

88196 

88252 

88309 

88366 

88423 

88480 

88536 

88593 

77 

88649 

88705 

88762 

88818 

88874 

88930 

88986 

89042 

89098 

89154 

78 

89209 

89265 

89321 

89376 

89432 

89487 

89542 

89597 

89653 

89708 

79 

89763 

89818 

89873 

89927 

89982 

90037 

90091 

90146 

90200 

90255 


































AGRICULTURAL SURVEYING LABORATORY 


93 


LOGARITHMS OF NUMBERS, FROM 0 TO 1000. 

( Continued. ) 


No. 

0 

1 ^ 

2 ' 

3 

4 

5 

6 

7 

8 

9 

80 

90309190363190417 

90472 

90526 

90580| 

90634 

90687 

90741 

90795 

81 

90849 

90902 

90956 

91009 

91062 

91116 

91169 

91222 

91275 

91328 

82 

91381 

91434 

91487 

91540 

91593 

91645 

91698 

91751 

91803 

91855 

83 

91908 

91960 

92012 

92065 

92117 

92169 

92221 

92273 

92324 

92376 

84 

92428 

92480 

92531 

92583 

92634 

92686 

92737 

92788 

92840 

92891 

85 1 

92942 

92993 

93044 

93095 

93146 

93197 

93247 

93298 

93349 

93399 

86 

93450 

93500 

93551 

93601 

93651 

93702 

93752 

93802 

93852 

93902 

87 

93952 

94002 

94052 

94101 

94151 

94201 

94250 

94300 

94349 

94399 

88 

94448 

94498 

94547 

94596 

94645 

94694 

94743 

94792 

94841 

94890 

89 

94939 

94988 

95036 

95085 

95134 

95182 

95231 

95279 

95328 

95376 

90 

95424 

95472 

95521 

95569 

95617 

95665 

95713 

95761 

95809 

95856 

91 

95904 

95952 

95999 

96047 

96095 

96142 

96190 

96237 

96284 

96332 

92 

96379 

96426 

96473 

96520 

96567 

96614 

96661 

96708 

96755 

96802 

93 

96848 

96895 

96942 

96988 

97035 

97081 

97128 

97174 

97220 

97267 

94 

97313 

97359 

97405 

97451 

97497 

97543 

97589 

97635 

97681 

97727 

95 

97772 

97818 

97864 

97909 

97955 

98000 

98046 

98091 

98137 

98182 

96 

98227 

98272 

98318 

98363 

98408 

98453 

98498 

98543 

98588 

98632 

97 

98677 

98722 

98767 

98811 

98856 

98900 

98945 

98989 

99034 

99078 

98 

99123 

99167 

99211 

99255 

99300 

99344 

99388 

99432 

99476 

99520 

99 

99564 

99607 

99651 

99695 

1 

99739 

99782 

99826 

99870 

99913 

99957 








































94 


AGRICULTURAL SURVEYING LABORATORY 


NATURAL SINES 


Deg . 

0 ' 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

Deg . 

0 

.0000 

.0029 

.0058 

.0087 

.0116 

.0145 

89 

1 

.0175 

.0204 

.0233 

.0262 

.0291 

.0320 

88 

2 

.0349 

.0378 

.0407 

.0436 

.0465 

.0494 

87 

3 

.0523 

.0552 

.0581 

.0610 

.0640 

.0669 

86 

4 

.0698 

.0727 

.0756 

.0785 

.0814 

.0843 

85 

5 

.0872 

.0901 

.0929 

.0958 

.0987 

.1016 

84 

6 

.1045 

.1074 

.1103 

.1132 

.1161 

.1190 

83 

7 

.1219 

.1248 

.1279 

.1305 

.1334 

.1363 

82 

8 

.1392 

.1421 

.1449 

.1478 

.1507 

.1536 

81 

9 

.1564 

.1593 

.1622 

.1650 

.1679 

.1708 

80 

10 

.1736 

.1765 

.1794 

.1822 

.1851 

.1880 

79 

11 

.1908 

.1937 

.1965 

.1994 

.2022 

.2051 

78 

12 

.2079 

.2108 

.2136 

.2164 

.2193 

.2221 

77 

13 

.2250 

.2278 

.2306 

.2334 

.2363 

.2391 

76 

14 

.2419 

.2447 

.2476 

.2504 

.2532 

.2560 

75 

15 

.2588 

.2616 

.2644 

.2672 

.2700 

.2728 

74 

16 

.2756 

.2784 

.2812 

.2840 

.2868 

.2890 

73 

17 

.2924 

.2952 

.2979 

.3007 

.3035 

.3062 

72 

18 

.3090 

.3118 

.3145 

.3173 

.3201 

.3228 

71 

19 

.3256 

.3283 

.3311 

.3338 

.3365 

.3393 

70 

20 

.3420 

.3448 

.3475 

.3502 

.3529 

.3557 

69 

21 

.3584 

.3611 

.3638 

.3665 

.3692 

.3719 

68 

22 

.3746 

.3773 

.3800 

.3827 

.3854 

.3881 

67 

23 

.3907 

.3934 

.3961 

.3987 

,4014 

.4041 

66 

24 

.4067 

.4094 

.4120 

.4147 

.4173 

.4200 

65 

25 

.4226 

.4253 

.4279 

.4305 

.4331 

.4358 

64 

26 

.4384 

.4410 

.4436 

.4462 

.4488 

.4514 

63 

27 

.4540 

.4566 

.4592 

.4617 

.4643 

.4669 

62 

28 

.4695 

.4720 

.4746 

.4772 

.4797 

.4823 

61 

29 

.4848 

.4874 

.4899 

.4924 

.4950 

.4975 

60 

30 

.5000 

.5025 

.5050 

.5075 

.5100 

.5125 

59 

31 

.5150 

.5175 

.5200 

.5225 

.5250 

.6275 

68 

Deg . 

60 ' 

50 ' 

40 ' 

1 30 ' 

20 ' 

10 ' 

Deg . 

i 


NATURAL COSINES 
















































AGRICULTURAL SURVEYING LABORATORY 


95 


NATURAL SINES 

( Continued.) 


Deg . 

0 ' 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

Deg . 

32 

.5299 

.5324 

.5348 

.5373 

.5398 

.5422 

57 

33 

.5446 

.5471 

.5495 

.5519 

.5544 

.5568 

56 

34 

.5592 

.5616 

.5640 

.5664 

.5688 

.5712 

55 

35 

.5736 

.5760 

.5783 

.5807 

.5831 

.5854 

54 

36 

.5878 

.5901 

.5925 

.5948 

.6972 

.5995 

53 

37 

.6018 

.6041 

.6065 

.6088 

.6111 

.6134 

62 

38 

.6157 

.6180 

.6202 

.6225 

.6248 

.6271 

51 

39 

.6293 

.6316 

.6338 

.6361 

.6383 

.6406 

50 

40 

.6428 

.6450 

.6472 

.6494 

.6517 

.6539 

49 

41 

.6561 

.6583 

.6604 

.6626 

.6648 

.6670 

48 

42 

.6691 

.6713 

.6734 

.6756 

.6777 

6799 

47 

43 

.6820 

.6841 

.6862 

.6884 

.6905 

.6926 

46 

44 

.6947 

.6967 

.6988 

.7009 

.7030 

.7050 

45 

45 

.7071 

.7092 

.7112 

.7133 

.7153 

.7173 

44 

46 

.7193 

.7214 

.7234 

.7254 

.7274 

.7294 

43 

47 

.7314 

.7333 

.7353 

.7373 

.7392 

.7412 

42 

48 

.7431 

.7451 

.7470 

.7490 

.7509 

.7528 

41 

49 

.7547 

.7566 

.7585 

.7604 

.7623 

.7642 

40 

50 

.7660 

.7679 

.7698 

.7716 

.7735 

.7753 

39 

51 

.7771 

.7790 

.7808 

.7826 

.7844 

.7862 

38 

52 

.7880 

.7898 

.7916 

.7934 

.7951 

.7969 

37 

53 

.7986 

.8004 

.8021 

.8039 

.8056 

.8073 

36 

54 

.8090 

.8107 

.8124 

.8141 

.8158 

.8175 

35 

55 

.8192 

.8208 

.8225 

.8241 

.8258 

.8274 

34 

56 

.8290 

.8307 

.8323 

.8339 

.8355 

.8371 

33 

57 

.8387 

.8403 

.8418 

.8434 

.8450 

.8465 

32 

58 

.8480 

.8496 

.8511 

.8526 

.8542 

.8557 

31 

59 

.8572 

.8587 

.8601 

.8616 

.8631 

.8646 

30 

1 

60 

.8660 

.8675 

.8689 

.8704 

.8718 

.8732 

29 

61 

.8746 

.8760 

.8774 

.8788 

.8802 

.8816 

28 

Deg . 

60 ' j 

50 ' | 

40 ' 

30 ' 

20 ' 

10 ' 

Deg . 


NATURAL COSINES 



































96 AGRICULTURAL SURVEYING LABORATORY 


NATURAL SINES 


( Continued.) 


Deg. 

0' 

10' 

20' 

30' 

40' 

50' 

Deg. 

62 

.8829 

.8843 

.8857 

.8870 

1 

.8884 

.8897 

27 

63 

.8910 

.8923 

.8936 

.8949 

.8962 

.8975 

26 

64 

.8988 

.9001 

.9013 

.9026 

.9038 

.9051 

25 

65 

.9063 

.9075 

.9088 

.9100 

.9112 

.9124 

24 

66 

.9135 

.9147 

.9159 

.9171 

.9182 

.9194 

23 

67 

.9205 

.9216 

.9228 

.9239 

.9250 

.9261 

22 

68 

.9272 

.9283 

.9293 

.9304 

.9315 

.9325 

21 

69 

.9336 

.9346 

.9356 

.9367 

.9377 

.9387 

20 

70 

.9397 

.9407 

.9417 

.9426 

.9436 

.9446 

19 

71 

.9455 

.9465 

.9474 

.9483 

.9492 

.9502 

18 

72 

.9511 

.9520 

.9528 

.9537 

.9546 

.9555 

17 

73 

.9563 

.9572 

.9580 

.9588 

.9596 

.9605 

16 

74 

.9613 

.9621 

.9628 

.9636 

.9644 

.9652 

15 

75 

.9659 

.9667 

.9674 

.9681 

.9689 

.9696 

14 

76 

.9703 

.9710 

.9717 

.9724 

.9730 

.9737 

13 

77 

.9744 

.9750 

.9757 

.9763 

.9769 

.9775 

12 

78 

.9781 

.9787 

.9793 

.9799 

.9805 

.9811 

11 

79 

.9816 

.9822 

.9827 

.9833 

.9838 

.9843 

10 

80 

.9848 

.9853 

.9858 

.9863 

.9868 

.9872 

9 

81 

.9877 

.9881 

.9886 

.9890 

.9894 

.9899 

8 

82 

.9903 

.9907 

.9911 

.9914 

.9918 

.9922 

7 

83 

.9925 

.9929 

.9932 

.9936 

.9939 

.9942 

6 

84 

.9945 

.9948 

.9951 

.9954 

.9957 

.9959 

5 

85 

.9962 

.9964 

.9967 

.9969 

.9971 

.9974 

4 

86 

.9976 

.9978 

.9980 

.9981 

.9983 

.9985 

3 

87 

.9986 

.9988 

.9989 

.9990 

.9992 

.9993 

2 

88 

.9994 

.9995 

.9996 

.9997 

.9997 

.9998 

1 

89 

.9989 

.9999 

.9999 

.9999 

1.0000 

1.0000 

0 

Deg. 

j 60' 

j 50' 

J 40' 

30' 

20' 

1 10r 

Deg. 


NATURAL COSINES 


























AGRICULTURAL SURVEYING LABORATORY 


97 


NATURAL TANGENTS 


Deg. 

0' 

10' 

1 

20' j 

30' 

40' 

50' 

Deg. 

0 

.0000 

.0029 

.0058 

.0087 

.0116 

.0145 

89 

1 

.0175 

.0204 

.0233 

.0262 

.0291 

.0320 

88 

2 

.0349 

.0378 

.0407 

.0437 

.0466 

.0495 

87 

3 

.0524 

.0553 

.0582 

.0612 

.0641 

.0670 

86 

4 

.0699 

.0729 

.0758 

.0787 

.0816 

.0846 

85 

5 

.0875 

.0904 

.0934 

.0963 

.0992 

.1022 

84 

6 

.1051 

.1080 

.1110 

.1139 

.1169 

.1198 

83 

7 

.1228 

.1257 

.1287 

.1317 

.1346 

.1376 

82 

8 

.1405 

.1435 

.1465 

.1495 

.1524 

.1554 

81 

9 

.1584 

.1614 

.1644 

.1673 

.1703 

.1733 

80 

10 

.1763 

.1793 

.1823 

.1853 

.1883 

.1914 

79 

11 

.1944 

.1974 

.2004 

.2035 

.2065 

.2095 

78 

12 

.2126 

.2156 

.2186 

.2217 

.2247 

.2278 

77 

13 

.2309 

.2339 

.2370 

.2401 

.2432 

.2462 

76 

14 

.2493 

.2524 

.2555 

.2586 

.2617 

.2648 

75 

15 

.2679 

.2711 

.2742 

.2773 

.2805 

.2836 

74 

16 

.2867 

.2899 

.2931 

.2962 

.2994 

.3026 

73 

17 

.3057 

.3089 

.3121 

.3153 

.3185 

.3217 

72 

18 

.3249 

.3281 

.3314 

.3346 

.3378 

.3411 

71 

19 

.3443 

.3476 

.3508 

.3541 

1 

.3574 

.3607 

70 

20 

.3640 

.3673 

.3706 

.3739 

.3772 

.3805 

69 

21 

.3839 

.3872 

.3906 

.3939 

.3973 

.4006 

68 

22 

.4040 

.4074 

.4108 

.4142 

.4176 

.4210 

67 

23 

.4245 

.4279 

.4314 

.4348 

.4383 

.4417 

66 

24 

.4452 

.4487 

.4522 

.4557 

.4592 

.4628 

65 

25 

.4663 

.4699 

.4734 

.4770 

.4806 

.4841 

64 

26 

.4877 

.4913 

.4950 

.4986 

.5022 

.5059 

63 

27 

.5095 

.5132 

.5169 

.5206 

.5243 

.5280 

62 

28 

.5317 

.5354 

.5392 

.5430 

.5467 

.5505 

61 

29 

.5543 

.5581 

.5619 

.5658 

.5696 

.5735 

60 

30 

.5774 

.5812 

.5851 

.5890 

.5930 

.5969 

59 

31 

.6009 

.6048 

.6088 

.6128 

.6168 

.6208 

58 

Deg. 

60' 

50' 

40' 

30' 

1 

20' 

1 

10' 

Deg. 


NATURAL COTANGENTS 


































































98 


AGRICULTURAL SURVEYING LABORATORY 


NATURAL TANGENTS 


( Continued.) 


Deg. 

0' 

10' 

20' 

30' 

40' 

50' 

Deg. 

32 

.6249 

.6289 

.6330 

.6371 

.6412 

.6453 

57 

33 

.6494 

.6536 

.6577 

.6619 

.6661 

.6703 

56 

34 

.6745 

.6787 

.6830 

.6873 

.6916 

.6959 

55 

35 

.7002 

.7040 

.7089 

.7133 

.7177 

.7221 

54 

36 

.7265 

.7310 

.7355 

.7400 

.7445 

.7490 

53 

37 

.7536 

.7581 

.7627 

.7673 

.7720 

.7766 

52 

38 

.7813 

.7860 

.7907 

.7954 

.8002 

.8050 

51 

39 

.8098 

.8146 

.8195 

.8243 

.8292 

.8342 

50 

40 

.8391 

.8441 

.8491 

.8541 

.8591 

.8642 

I 

49 

41 

.8693 

.8744 

.8796 

.8847 

.8899 

.8952 

48 

42 

.9004 

.9057 

.9110 

.9163 

.9217 

.9271 

47 

43 

.9325 

.9380 

.9435 

.9490 

.9545 

.9601 

46 

44 

.9657 

.9713 

.9770 

.9827 

.9884 

.9942 

45 

45 

1.0000 

1.0058 

1.0117 

1.0176 

1.0235 

1.0295 

44 

46 

1.0355 

1.0416 

1.0477 

1.0533 

1.0599 

1.0661 

43 

47 

1.0724 

1.0786 

1.0850 

1.0913 

.10977 

1.1041 

42 

48 

1.1106 

1.1171 

1.1237 

1.1303 

1.1369 

1.1436 

41 

49 

1.1504 

1.1571 

1.1640 

1.1708 

1.1778 

1.1847 

40 

50 

1.1918 

1.1988 

1.2059 

1.2131 

1.2203 

1.2276 

39 

51 

1.2349 

1.2423 

1.2497 

1.2572 

1.2647 

1.2723 

38 

52 

1.2799 

1.2876 

1.2954 

1.3032 

1.3111 

1.3190 

37 

53 

1.3270 

1.3351 

1.3452 

1.3514 

1.3597 

1.3680 

36 

54 

1.3764 

1.3848 

1.3934 

1,4019 

1.4106 

1.4193 

35 

55 

1.4281 

1,4370 

1.4460 

1,4550 

1,4641 

1,4733 

34 

56 

1.4826 

1.4919 

1.5013 

1.5108 

1.5204 

1.5301 

33 

57 

1.5399 

1.5497 

1.5597 

1.5697 

1.5798 

1.5900 

32 

58 

1.6003 

1.6107 

1.6212 

1.6319 

1.6426 

1.6534 

31 

59 

» 

1.6643 

1.6753 

1.6864 

1.6977 

1.7090 

1.7205 

30 

60 

1.7321 

1.7437 

1.7556 

1.7675 

1.7797 

1.7917 

29 

61 

1.8040 

1.8165 

1.8291 

1.8418 

1.8546 

1.8676 

28 

Deg. 

60' 

50' | 

40' | 

30' 1 

20' 

L 

10' 

Deg. 


NATURAL COTANGENTS 






















































AGRICULTURAL SURVEYING LABORATORY 99 


NATURAL TANGENTS 


( Continued.) 


Deg. 

0' 

10' 

20' 

r 

30' 

40' 

50' 

Deg. 

62 

1.8807 

1.8940 

1.9074 

1.9210 

1.9347 

1.9486 

27 

63 

1.9626 

1.9768 

1.9912 

2.0057 

2.0204 

2.0353 

26 

64 

2.0503 

2.0655 

2.0809 

2.0965 

2.1123 

2.1283 

25 

65 

2.1445 

2.1609 

2.1775 

2.1943 

2.2113 

2.2286 

24 

66 

2.2460 

2.2637 

2.2817 

2.2998 

2.3183 

2.3369 

23 

67 

2.3559 

2.3750 

2.3945 

2.4142 

2.4342 

2.4545 

22 

68 

2.4751 

2.4960 

2.5172 

2.5386 

2.5605 

2.5826 

21 

69 

2.6051 

2.6279 

2.6511 

2.6746 

2.6985 

2.7228 

20 

70 

2.7475 

2.7725 

2.7980 

2.8239 

2.8502 

2.8770 

19 

71 

2.9042 

2.9319 

2.9600 

2.9887 

3.0178 

3.0475 

18 

72 

3.0777 

3.1084 

3.1397 

3.1716 

3.2041 

3.2371 

17 

73 

3.2709 

3.3052 

3.3402 

3.3759 

3.4124 

3.4495 

16 

74 

3.4874 

3.5261 

3.5656 

3.6059 

3.6470 

3.6891 

15 

75 

3.7321 

3.7760 

3.8208 

3.8657 

3.9136 

3.9617 

14 

76 

4.0108 

4.0611 

4.1126 

4.1653 

4.2193 

4.2747 

13 

77 

4.3315 

4.3897 

4.4494 

4.5107 

4.5736 

4.6382 

12 

78 

4.7046 

4.7729 

4.8430 

4.9152 

4.9894 

5.0658 

11 

79 

5.1446 

5.2257 

5.3093 

5.3955 

5.4845 

5.5764 

10 

80 

5.6713 

5.7694 

5.8708 

5.9758 

6.0844 

6.1970 

9 

81 

6.3138 

6.4348 

6.5606 

6.6912 

6.8269 

6.9682 

8 

82 

7.1154 

7.2687 

7.4287 

7.5958 

7.7704 

7.9530 

7 

83 

8.1443 

8.3450 

8.5555 

8.7769 

9.0098 

9.2553 

6 

84 

9.5144 

9.7882 

10.078 

10.385 

10.711 

11.059 

5 

85 

11.430 

11.826 

12.250 

12.706 

13.197 

13.727 

4 

86 

14.300 

14.924 

15.605 

16.350 

17.169 

18.075 

3 

87 

19.081 

20.206 

21.470 

22.903 

24.542 

26.432 

2 

88 

28.636 

31.242 

34.368 

38.189 

42.964 

49.104 

1 I 

89 

57.290 

68.750 

85.940 

114.588 

171.885 

343.77 

0 | 

1 

Deg. 

60' 

50' 

40' j 

30' j 

20' | 

10' 

Deg. 


NATURAL COTANGENTS 














































■ 













































* 



















































































Deacidified using the Bookkeeper process 
Neutralizing agent: Magnesium Oxide 
Treatment Date: Jan. 2004 

PreservationTechnologies 

A WORLD LEADER IN PAPER PRESERVATION 

111 Thomson Park Drive 
Cranberry Township, PA 16066 
(724) 779-2111 











